Fourier and beyond: invariance properties of a family of integral transforms (Q2360576)
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| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Fourier and beyond: invariance properties of a family of integral transforms |
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Fourier and beyond: invariance properties of a family of integral transforms (English)
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4 July 2017
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It is shown that the classical Fourier transform on the real line can be uniquely characterized by an intertwining relation with dilations and by having a Gaussian as an eigenfunction. The results extend to diverse Fourier type transforms with this property. Short-time analogues of these transforms are established and their properties are studied.
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Fourier transform
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Gaussian
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integral transform
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Fourier-Bessel transform
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unitarity
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short-time transform
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